U.S. patent number 9,297,638 [Application Number 14/520,057] was granted by the patent office on 2016-03-29 for two-path plasmonic interferometer with integrated detector.
This patent grant is currently assigned to Research Foundation of The City of New York, Sandia Corporation. The grantee listed for this patent is Gregory Aizin, Sandia Corporation. Invention is credited to Gregory Aizin, Gregory Conrad Dyer, Eric A. Shaner.
United States Patent |
9,297,638 |
Dyer , et al. |
March 29, 2016 |
Two-path plasmonic interferometer with integrated detector
Abstract
An electrically tunable terahertz two-path plasmonic
interferometer with an integrated detection element can down
convert a terahertz field to a rectified DC signal. The integrated
detector utilizes a resonant plasmonic homodyne mixing mechanism
that measures the component of the plasma waves in-phase with an
excitation field that functions as the local oscillator in the
mixer. The plasmonic interferometer comprises two independently
tuned electrical paths. The plasmonic interferometer enables a
spectrometer-on-a-chip where the tuning of electrical path length
plays an analogous role to that of physical path length in
macroscopic Fourier transform interferometers.
Inventors: |
Dyer; Gregory Conrad
(Albuquerque, NM), Shaner; Eric A. (Rio Rancho, NM),
Aizin; Gregory (East Brunswick, NJ) |
Applicant: |
Name |
City |
State |
Country |
Type |
Sandia Corporation
Aizin; Gregory |
Albuquerque
East Brunswick |
NM
NJ |
US
US |
|
|
Assignee: |
Sandia Corporation
(Albuquerque, NM)
Research Foundation of The City of New York (New York,
NY)
|
Family
ID: |
55537417 |
Appl.
No.: |
14/520,057 |
Filed: |
October 21, 2014 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01L
31/035236 (20130101); G01N 21/45 (20130101); G01B
9/02049 (20130101); G01V 8/005 (20130101); H01L
31/1129 (20130101); H01L 31/035209 (20130101); G01N
21/3581 (20130101); G01B 9/02001 (20130101); H01Q
15/02 (20130101); B82Y 20/00 (20130101); B82Y
30/00 (20130101) |
Current International
Class: |
G01J
5/02 (20060101); G01B 9/02 (20060101) |
Field of
Search: |
;250/353 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
WF. Andress et al., "Ultra-Subwavelength Two-Dimensional Plasmonic
Circuits", Nano Letters, vol. 12 (2012), pp. 2272-2277. cited by
applicant .
K.Y.M. Yeung et al. "Two-Path Solid-State Interferometry Using
Ultra-Subwavelength Two-Dimensional Plasmonic Waves", Applied
Physics Letters 102 (2013), pp. 021104-1-021104-4. cited by
applicant .
S. Rosenblatt et al., "Mixing at 50 GHz Using a Single-Walled
Carbon Nanotube Transistor", Applied Physics Letters 87 (2005), pp.
153111-1-153111-3. cited by applicant .
V.M. Muravev et al., "Plasmonic Detector/Spectrometer of
Subterahertz Radiation Based on Two-Dimensional Electron System
with Embedded Defect", Applied Physics Letters 100 (2012), pp.
082102-1-082102-3. cited by applicant .
G.C. Dyer et al., "A Terahertz Plasmon Cavity Detector", Applied
Physics Letters 97 (2010), pp. 193507-1-193507-3. cited by
applicant .
G.C. Dyer et al., "Enhanced Performance of Resonant Sub-Terahertz
Detection in a Plasmonic Cavity", Applied Physics Letters 100
(2012), pp. 083506-1-083506-4. cited by applicant .
G.C. Dyer et al., "Inducing an Incipient Terahertz Finite Plasmonic
Crystal in Coupled Two Dimensional Plasmonic Cavities", Physical
Review Letters 109 (2012), pp. 126803-1-126803-5. cited by
applicant .
G.C. Dyer et al., "Induced Transparency by Coupling of Tamm and
Defect States in Tunable Terahertz Plasmonic Crystals", Nature
Photonics, vol. 7 (2013), pp. 925-930. cited by applicant.
|
Primary Examiner: Makiya; David J
Assistant Examiner: Jo; Taeho
Attorney, Agent or Firm: Bieg; Kevin W.
Government Interests
STATEMENT OF GOVERNMENT INTEREST
This invention was made with Government support under contract no.
DE-AC04-94AL85000 awarded by the U. S. Department of Energy to
Sandia Corporation. The Government has certain rights in the
invention.
Claims
We claim:
1. A two-path plasmonic interferometer, comprising: a layer
providing a two-dimensional electron gas (2DEG) or two-dimensional
hole gas (2DHG); a source and a drain at opposing ends of the 2DEG
or 2DHG layer; a source-side gate, a central gate, and a drain-side
gate disposed on and separated from the 2DEG or 2DHG layer; and a
voltage source for applying a voltage independently to each of the
gates to spatially modulate the electron or hole density in the
2DEG or 2DHG layer under each gate, thereby providing a source-side
plasmonic path under the source-side gate and a drain-side
plasmonic path under the drain-side gate and a plasmonic mixer
under the central gate when the central gate is biased to near
depletion; wherein a standing plasma wave from the source-side
plasmonic path couples with a standing plasma wave from the
drain-side plasmonic path interfere at the plasmonic mixer to
provide a photoresponse when incident electromagnetic radiation is
coupled to the 2DEG or 2DHG layer.
2. The two-path plasmonic interferometer of claim 1, wherein the
incident electromagnetic radiation has a frequency of between 10
GHz and 60 THz.
3. The two-path plasmonic interferometer of claim 1, wherein the
source-side gate, central gate, and drain-side gate each comprise
one or more finger electrodes.
4. The two-path plasmonic interferometer of claim 1, wherein the
length of the source-side and drain-side plasmonic paths are each
less than 1/10 the free space wavelength of the incident
electromagnetic radiation.
5. The two-path plasmonic interferometer of claim 1, wherein the
source-side plasmonic path and the drain-side plasmonic path have
equal plasmonic lengths.
6. The two-path plasmonic interferometer of claim 1, wherein the
2DEG or 2DHG density under the central gate electrode is
sufficiently depleted so that the coherence length of the plasmonic
excitation is less than the length of the mixing region under the
central gate.
7. The two-path plasmonic interferometer of claim 1, wherein the
layer providing the 2DEG is formed at a semiconductor
heterojunction formed between two semiconductor materials having
different band gaps.
8. The two-path plasmonic interferometer of claim 7, wherein the
heterojunction comprises a III-V heterojunction.
9. The two-path plasmonic interferometer of claim 8, wherein the
III-V heterojunction comprises GaAs/AlGaAs, InGaAs/InAlAs,
GaN/AlGaN, or GaSb/InAs.
10. The two-path plasmonic interferometer of claim 1, wherein the
layer providing the 2DEG or 2DHG comprises an atomically thin
material having high electron mobility or high hole mobility.
11. The two-path plasmonic interferometer of claim 10, wherein the
atomically thin material having high electron mobility comprises
graphene.
12. The two-path plasmonic interferometer of claim 1, further
comprising an antenna to couple the incident electromagnetic
radiation to the 2DEG or 2DHG layer.
13. The two-path plasmonic interferometer crystal of claim 1,
further comprising a waveguide to couple the incident
electromagnetic radiation to the 2DEG or 2DHG layer.
14. The two-path plasmonic interferometer crystal of claim 1,
further comprising a hyper-hemispherical lens to couple the
incident electromagnetic radiation to the 2DEG or 2DHG layer.
15. The two-path plasmonic interferometer of claim 1, wherein the
photoresponse is a rectified DC voltage signal measured between the
source and the drain.
16. The two-path plasmonic interferometer of claim 15, further
comprising means for varying the voltage of the sources-side gate
and the drain-side gate and measuring an interferogram of the
rectified DC voltage signal.
17. The two-path plasmonic interferometer of claim 16, further
comprising means for post-processing the interferogram to provide a
frequency domain spectrum of the incident electromagnetic
spectrum.
18. The two-path plasmonic interferometer of claim 1, further
comprising means for applying a local oscillator signal to the
plasmonic mixer that has a frequency detuned from the incident
electromagnetic radiation, thereby providing an intermediate
frequency difference signal.
19. The two-path plasmonic interferometer of claim 1, further
comprising a sample in the source-side or drain-side plasmonic
path.
20. The two-path plasmonic interferometer of claim 1, wherein the
source-side and drain-side plasmonic path lengths are each shorter
than a plasmon coherence length.
Description
FIELD OF THE INVENTION
The present invention relates to widely voltage tunable far- and
mid-infrared plasmonic devices and, in particular, to a two-path
plasmonic interferometer with an integrated detector.
BACKGROUND OF THE INVENTION
There has been significant recent interest in the development of
terahertz (THz) integrated circuits (ICs) and detectors based upon
two-dimensional electron gas (2DEG) systems in semiconductor
nanostructures and graphene. Because microwave and THz fields
coupled to a 2DEG excite plasma waves, plasmon-based field-effect
devices can operate well above f.sub.T, the cutoff frequency
determined by carrier transit times. See M. I. Dyakonov and M. S.
Shur, Phys. Rev. Lett. 71, 2465 (1993); M. I. Dyakonov and M. S.
Shur, IEEE Trans. on Electron Devices 43, 380 (1996); W. F. Andress
et al., Nano Lett. 12, 2272 (2012); P. J. Burke et al., Appl. Phys.
Lett. 76, 745 (2000); and M. J. W. Rodwell et al., IEEE Trans. on
Electron Devices 48, 2606 (2001). Overdamped plasmonic field-effect
transistors (FETs) have been fabricated from III-V, Si, and
graphene material systems and utilized for room temperature THz
detection. See D. Coquillat et al., Opt. Express 18, 6024 (2010);
S. Preu et al., IEEE Trans. on THz Sci. and Tech. 2, 278 (2012); M.
S. Vitiello et al., Nano Lett. 12, 96 (2011); A. D. Gaspare et al.,
Appl. Phys. Lett. 100, 203504 (2012); A. Pitanti et al., Appl.
Phys. Lett. 101, 141103 (2012); A. Lisauskas et al., J. Appl. Phys.
105, 114511 (2009); S. Boppel et al., Electronics Letters 47, 661
(2011); and L. Vicarelli et al., Nature Mater. 11, 865 (2012). To
exploit underdamped two-dimensional (2D) plasmons in III-V
heterostructures, cryogenic operation of a
high-electron-mobility-transistor (HEMT) is generally required. See
W. F. Andress et al., Nano Lett. 12, 2272 (2012); P. J. Burke et
al., Appl. Phys. Lett. 76, 745 (2000); X. G. Peralta et al., Appl.
Phys. Lett. 81, 1627 (2002); E. A. Shaner et al., Appl. Phys. Lett.
87, 193507 (2005); W. Knap et al., Appl. Phys. Lett. 81, 4637
(2002); and V. M. Muravev and I. V. Kukushkin, Appl. Phys. Lett.
100, 082102 (2012). Within this constraint, potential applications
such as THz plasmonic ICs and detectors based on III-V
heterostructures can be realized in these material systems.
However, as the quality of large-area graphene materials improves,
similar devices may emerge that operate in the mid-infrared at room
temperature.
SUMMARY OF THE INVENTION
The present invention is directed to a two-path plasmonic
interferometer, comprising a layer providing a two-dimensional
electron gas (2DEG) or two-dimensional hole gas (2DHG); a source
and a drain at opposing ends of the 2DEG or 2DHG layer; a
source-side gate, a central gate, and a drain-side gate disposed on
and separated from the 2DEG or 2DHG layer; and a voltage source for
applying a voltage independently to each of the gates to spatially
modulate the electron or hole density in the 2DEG or 2DHG layer
under each gate, thereby providing a source-side plasmonic path
under the source-side gate and a drain-side plasmonic path under
the drain-side gate and a plasmonic mixer under the central gate
when the central gate is biased to near depletion; wherein a
standing plasma wave from the source-side plasmonic path couples
with a standing plasma wave from the drain-side plasmonic path
interfere at the plasmonic mixer to provide a photoresponse when
incident electromagnetic radiation is coupled to the 2DEG or 2DHG
layer.
The incident electromagnetic radiation can have a frequency of
between 10 GHz and 60 THz (i.e., free space wavelength of between
30 mm and 5 .mu.m). The length of the source-side and drain-side
plasmonic paths can each be less than 1/10 the free space
wavelength of the incident electromagnetic radiation and can have
equal plasmonic lengths. A sample can be placed in one of the
balanced plasmonic paths to enable interferometric spectroscopy of
the sample. An antenna and/or a hyper-hemispherical lens can couple
the incident electromagnetic radiation to the 2DEG or 2DHG layer.
Alternatively, the incident electromagnetic radiation can be
coupled into the 2DEG or 2DHG layer via on-chip waveguides. When
used as a homodyne mixer, the photoresponse is a rectified DC
voltage signal measured between the source and the drain terminals.
The voltages to the source-side and drain-side gates can be varied
to obtain an interoferogram from the rectified DC signal. The
interferogram can be post-processed to provide a frequency domain
spectrum of the incident electromagnetic spectrum. Alternatively,
the two-path plasmonic interferometer can be used as a heterodyne
mixer by applying a local oscillator signal to the plasmonic mixer
that has a frequency detuned from the incident electromagnetic
radiation, thereby providing an intermediate frequency difference
signal.
BRIEF DESCRIPTION OF THE DRAWINGS
The detailed description will refer to the following drawings,
wherein like elements are referred to by like numbers.
FIG. 1 is a diagram of the layout of an optical Mach-Zehnder
interferometer where the electromagnetic properties of Path D and
Path S are independently defined.
FIG. 2(a) is a side-view schematic illustration of a sub-wavelength
plasmonic interferometer with integrated detector. FIG. 2(b) is a
top-view schematic illustration of the plasmonic interferometer
further comprising an antenna for coupling incident radiation in
the 2DEG layer.
FIG. 3(a) is a top-view scanning electron micrograph (SEM) of a
two-path plasmonic interferometer where gate G2 of a HEMT defines
the mixing element and Path S and Path D are tuned by G1 and G3,
respectively. FIGS. 3(b) and 3(c) are SEMs of the same
interferometer, but with G1 and G3, respectively, defining the
mixing region.
FIG. 4 is an equivalent circuit schematic for a two-path plasmonic
interferometer where Path D and Path S are independently
tunable.
FIG. 5(a) is a plot of the channel conductance at 8 K of the HEMT
illustrated in FIG. 3 plotted as a function of voltage applied to
gate G1. FIG. 5(b) is a plot of the product
.times..differential..differential..times..times. ##EQU00001##
calculated using the channel conductance measured at 8 K, as a
function of voltage applied to G1. FIG. 5(c) is a plot of the 8 K
device photoresponse under 0.270 THz illumination as a function of
voltage applied to G1.
FIG. 6(a) is a plot of the product
.times..differential..differential..times..times. ##EQU00002##
plotted as a function of voltage V.sub.Gj applied to gates G1, G2,
and G3, calculated using the channel conductance measured at 8 K of
the HEMT illustrated in FIG. 3. FIG. 6(b) is a plot of the 8 K
device photoresponse under 0.270 THz illumination as a function of
voltage applied to gates G1, G2, and G3.
FIGS. 7(a) and 7(b) are plots of the photoresponse under 0.270 THz
and 0.330 THz excitation at 8 K, respectively, as a function of the
electrical lengths of Path S, .theta..sub.S, and Path D,
.theta..sub.D with G2 defining the mixing region of the HEMT as
illustrated in FIG. 3(a). FIGS. 7(c) and 7(d) show model
calculations of the photoresponse under 0.270 THz and 0.330 THz
excitation, respectively, plotted using a transmission line
formalism to describe the independent signals from Paths S and D
coupled to the mixing element below G2.
FIG. 8(a) is a scanning electron micrograph of a two-path plasmonic
crystal interferometer where gate G2 of the HEMT defines the mixing
element and Path S and Path D are tuned by G1 and G3, respectively.
FIG. 8(b) is a plot of the 8 K device photoresponse under 0.345 THz
illumination, mapped as a function of voltage applied to gates G1
and G3 with G2 fixed at -2.80 V in the left frame. A model
calculation of the photoresponse under 0.345 THz illumination is
also plotted in the right frame using a transmission line formalism
to describe the independent signals from Paths S and D coupled to
the mixing element below G2.
FIG. 9(a) is a schematic layout of a coplanar waveguide-based
plasmonic interferometer device. Three ports with a
ground-signal-ground configuration allow for coupling of signals
RF.sub.D and RF.sub.S and a local oscillator LO to the plasmonic
interferometer (dashed outline region). A directional coupler can
be used to route the resulting intermediate frequency signal (IF)
to a spectrum analyzer. FIG. 9(b) shows detail of the plasmonic
interferometer device and the DC and RF biases.
FIG. 10(a) is a graph of Q-factor of the plasmon as a function of
frequency at five different normalized 2DEG densities for an
exemplary GaAs/AlGaAs double quantum well heterostructure. FIG.
10(b) is a graph of the coherence length.
DETAILED DESCRIPTION OF THE INVENTION
The present invention is directed to a two-dimensional (2D)
plasmonic interferometer with an integrated resonant homodyne
mixing element based upon a HEMT with multiple gate terminals.
Biasing a gate in a HEMT near its threshold voltage while
illuminated by radiation near the 2D plasma frequency effectively
produces a plasmonic homodyne mixing element and enables phase
sensitive detection of plasma waves. When multiple plasmonic
cavities are coupled to this gate-induced plasmonic mixing element,
the device can provide a sub-wavelength two-path interferometer
with an integrated on-chip detector where the paths can be
independently tuned. See W. F. Andress et al, Nano Lett. 12, 2272
(2012); and K. Y. M. Yeung et al., Appl. Phys. Lett. 102, 021104
(2013). Unlike standard homodyne mixing techniques, plasmonic
homodyne mixing permits near-field detection well above the
conventional RC-limited bandwidth of devices at their operational
bias. See S. Rosenblatt et al., Appl. Phys. Lett. 87, 153111
(2005).
To describe the underlying mechanism of the solid-state plasmonic
interferometer of the present invention, it is useful to first draw
an analogy to an optical Mach-Zehnder interferometer. An optical
Mach-Zehnder interferometer can be used to determine the relative
phase shift variations between two collimated beams derived by
splitting light from a single source. An optical Mach-Zehnder
interferometer, comprising optical Path D and optical Path S, is
diagrammed in FIG. 1. Beam splitters are labeled BS1 and BS2 and
mirrors are labeled MD and MS. Each optical path has a region of
length d where the permittivity (.epsilon..sub.D, .epsilon..sub.S)
and permeability (.mu..sub.D, .mu..sub.S) of the electromagnetic
medium is independently defined. If the phase velocity in these
regions is given by .nu..sub.D,S=1/ {square root over
(.epsilon..sub.D,S.mu..sub.D,S)}, then the phase difference of
beams on these two paths is
.theta..sub.D-.theta..sub.S=.omega.d(.nu..sub.D.sup.-1-.nu..sub.S.sup.-1)-
. This phase difference results not from a difference in path
lengths (i.e., .DELTA.d=0), but instead from a difference in the
phase velocities along sections of the two paths (i.e.,
.nu..sub.D.noteq..nu..sub.S). When the permittivity, permeability,
or both, are tunable, then so are the phase velocities .nu..sub.D,S
of these regions and consequently the phase difference
.theta..sub.D-.theta..sub.S between the two paths. For example, the
Mach-Zehnder interferometer can be used to measure phase shifts
between the two split beams caused by a sample that modifies the
permittivity and/or permeability in one of the optical paths.
Readout in this diagram can be accomplished using a mixer to
produce a DC signal at the second beamsplitter BS2 where the
recombined beams are 180 degrees out of phase.
FIG. 2(a) is a schematic side-view illustration of a sub-wavelength
plasmonic interferometer with integrated detector of the present
invention. The interferometer is based upon a high-mobility
two-dimensional electron gas (2DEG) or two-dimensional hole gas
(2DHG). A 2DEG is used for simplicity to describe the invention
below, but the concepts apply similarly to a 2DHG. The 2DEG can be
a layer comprising a gas of electrons free to move in two
dimensions, but tightly confined in the third dimension. For
example, the 2DEG layer can comprise a semiconductor heterojunction
or an atomically thin material having high electron mobility formed
on a substrate or as a suspended membrane. A source-side gate G1, a
center gate G2, and a drain-side gate G3 are disposed on and
separated from the 2DEG layer by a thin spacer layer. For example,
the gates G1, G2, and G3 can be separated from the 2DEG layer by a
semiconducting or insulating layer. Each of the gates G1, G2, and
G3 can comprise one or more parallel finger electrodes. A voltage
can be applied to a gate to spatially modulate the electron density
in the 2DEG layer underlying the gate. A source S and a drain D can
be formed at the opposing ends of the 2DEG layer to provide
electrical contact to the structure. For interferometric
applications, the gaps between metallic terminals, e.g. between S
and G1 and G1 and G2, may be filled with a sample material. A
potential location of sample placement is indicated in FIG. 2(a) by
arrows. Just as the gates above the 2DEG layer modify plasmon
propagation by screening effects, 2D plasmons are sensitive to
other changes in local environment.
In a typical HEMT design, the drain D and source S contact are
designed to provide conductive, low resistance electrical contact
between the fabricated metal electrodes and the 2DEG. This follows
the accepted naming convention of D and S contacts used for field
effect transistors. However, D and S are more broadly applied in
the present invention. D and S imply a preferential flow of
electrical current through the 2DEG, while in the present invention
there is no applied electrical current required for operation.
Additionally, D and S can apply to non-conductive contacts at the
end of the 2DEG in the context of this invention.
The integrated detector is a plasmonic mixing element. This mixing
element can comprise a region of 2DEG with reduced or fully
depleted 2DEG. See U.S. Pat. No. 7,376,403 to Wanke et al., which
is incorporated herein by reference. When no electrical current is
passed through the 2DEG, this detector functions as a plasmonic
homodyne mixer. However, integration of an extrinsic mixing element
such as a Schottky diode with a semiconductor heterojunction device
is also possible. See U.S. Pat. No. 8,274,058 to Wanke et al.,
which is incorporated herein by reference. The underlying
requirement is that the near field of the plasma excitations
couples with the integrated mixer. Device-specific implementation
can vary provided this requirement is satisfied.
A 2DEG can be formed at a heterojunction between two semiconductors
having different band gaps. The heterojunction can comprise a
wide-bandgap semiconductor heavily doped with an electron donor,
such as n-type AlGaAs or n-type AlGaN, and an undoped narrow
bandgap semiconductor, such as GaAs or GaN. For example, the
heterojunction can be fabricated using molecular beam epitaxy. A
semiconductor heterojunction is preferably grown on a
semi-insulating and atomically flat substrate. The heterojunction
thereby forms a quantum well in the conduction band of the undoped
semiconductor. Electrons from the n-type semiconductor drop into
the quantum well and can move with high mobility without colliding
with impurities in the undoped semiconductor. A thin layer
comprising highly mobile conducting electrons with very high
concentration--the 2DEG--is thereby created at the heterojunction.
Other III-V heterojunctions can also be used, including but not
limited to GaAs/AlGaAs, InGaAs/InAlAs, and GaN/AlGaN.
Alternatively, a quantum well formed in a narrow gap semiconductor
placed between wide gap semiconductors with remote n-type dopants
can similarly provide a suitable 2DEG. Multiple quantum wells can
also be employed to increase the total 2DEG density through
summation of the densities in adjacent wells. Choice of the type of
heterojunction or quantum well can impact 2DEG mobility and density
as well as the depth of the well relative to the surface or the
epitaxial growth. The depth of the embedded 2DEG layer ultimately
determines the strength of plasmon screening due to fabricated
metal terminals. Finally, type-II heterojunctions, such as those
formed between InAs/GaSb, can produce a 2DEG which will differ
greatly in majority carrier effective mass.
A 2DEG can also be formed in atomically thin materials having high
electron mobility, such as graphene. Graphene is a one-atom thick
layer of sp.sup.2-bonded carbon arranged in a regular hexagonal
pattern. As such, graphene can be considered as an indefinitely
large polycyclic aromatic hydrocarbon in which electrons are free
to move by virtue of the sp.sup.2 bonding. In particular, graphene
has been found to have remarkably high electron mobility at room
temperature due to the low defect scattering of intrinsic
graphene.
Alternatively, a two-dimensional hole gas (2DHG) having similar
properties to the 2DEG but with positive carrier charge polarity
can also be formed by chemical or electronic doping of graphene or
in heterojunction-based materials. See U.S. Pat. No. 9,105,791,
issued Aug. 11, 2015, which is incorporated herein by
reference.
The incident radiation can have a frequency between about 10 GHz
and 60 THz (i.e., free space wavelength of between 30 mm and 5
.mu.m). All three gates G1, G2, and G3 can be driven by the
incident electromagnetic radiation field. To achieve a two-path
interferometer, gate G2 can be biased to depletion. Gates G1 and G3
then control independent source-side and drain-side paths for
plasmonic standing waves to couple into the depleted region below
G2.
The source-side and drain-side plasmonic path lengths are each
shorter than a plasmon coherence length. A transmission line model,
as described in U.S. Pat. No. 9,105,791, can be adapted to include
plasmon damping by accounting for dissipation in the definitions of
the transmission line characteristic impedance and dispersion. For
calculating the plasmon Q-factor and propagation lengths, it is
sufficient to define the dispersion law as q=-i {square root over
(i.omega.C(i.omega.L+R))} where R accounts for the damping of the
plasma wave. This resistance includes not only the scattering rate
found from the Drude conductivity of the 2DEG, but also a radiative
damping contribution. For high mobility 2DEGs
(.mu..sub.mob>100,000 cm.sup.2/Vs), this radiation resistance is
a more significant damping mechanism than the intrinsic 2DEG
resistance. See S. A. Mikhailov, Phys. Rev. B 54, 10335 (1996). The
total resistance can be defined in terms of the mobility and
radiative scattering rates as,
.omega..times..times..times..times..times..tau..tau. ##EQU00003##
where
.tau..times..mu. ##EQU00004## and
.tau..mu..times..times..times..times..times..times. ##EQU00005##
Using only fundamental constants and known or measured quantities
(2DEG density, mobility, GaAs permittivity, carrier effective
mass), the resistance R can be calculated explicitly to estimate
the effects of dissipation upon the plasma wave.
To determine the plasmon Q-factor and propagation length from the
dispersion law defined above, it is convenient to rewrite the
dispersion law as q.ident..beta.+i.alpha.. Then the Q-factor can be
defined as,
.beta..times..times..alpha. ##EQU00006## with the propagation
length of the damped plasmon subsequently given by,
.beta..times..alpha. ##EQU00007## Both the Q-factor and propagation
length relate to power dissipation of the plasmon. For examining
coherent coupling effects, it is the coherence length that provides
the more salient figure of merit. The coherence length is twice the
propagation length,
.alpha. ##EQU00008##
Tuning of the gate voltages G1 and G3 controls the 2DEG inductance
and resistance, L.sub.j,R.sub.j.varies.1.gamma..sub.j. Here
.gamma..sub.j defines the normalized 2DEG density under the
j.sup.th gate in terms of the threshold voltage V.sub.th (where
n.sub.2DEG.fwdarw.0) and the applied gate voltages V.sub.Gj such
that .gamma..sub.j.ident.(V.sub.th-V.sub.Gj)/V.sub.th. In FIGS.
10(a) and 10(b), respectively the plasmon Q-factor and coherence
length L.sub.C calculated for a gated GaAs/AlGaAs 2DEG (with
carrier density of about 4.times.10.sup.11 cm.sup.-2 at 12 K) are
plotted as a function of frequency .nu. for several values of the
normalized carrier density .gamma.. The Q-factor of the plasma wave
is approximately 10-25 in the range of frequencies from 200-450
GHz, shown with vertical dashed lines, and increases modestly as
the normalized 2DEG density is lowered. The coherence length,
however, depends much more critically on both the normalized 2DEG
density and frequency. In this frequency range, the plasmon
coherence length varies from L.sub.C<30 .mu.m when .gamma.=1 (no
applied gate voltage to L.sub.C<20 .mu.m when .gamma.=0.2.
The depleted region below G2 functions as a plasmonic mixer in
which the standing plasma waves coupled from its left and right
`ports` effectively interfere. The incident THz field coupled
directly to G2 behaves as a local oscillator voltage
.delta.V.sub.LO while the plasma waves from below G1 and G3 act as
signals .delta.V.sub.S and .delta.V.sub.D coupled to the mixer. The
resultant homodyne mixing mechanism `down converts` the THz fields
to a DC signal .delta.V.sub.DS that can be read out through the
drain D and source S contacts. Not only does this down conversion
turn high frequency fields into a DC signal easily transmitted on
standard coax, but, for example, it can take place in a 10
micrometer long interferometer element that is 100.times. smaller
than the mm-wavelength of THz radiation in free space. With two
balanced paths, it is possible to perform interferometric
spectroscopy on-chip, analogous to a Fourier transform infrared
spectrometer. However, rather than mechanically tuning the path
length of a traditional optical interferometer, the effective
permittivity of the 2DEG interferometer paths can be changed by
electrically tuning the gate voltages of G1 and G3. Post processing
after measuring the interferogram (an FFT with other corrections)
can provide a frequency domain spectrum of incident radiation.
In FIG. 2(b) is shown a schematic top-view illustration of the
plasmonic interferometer. An antenna optimized for a particular
band can couple the incident electromagnetic radiation to the
interferometer at the antenna vertex in a quasi-optical
configuration. The incident field is coupled to the source and
drain terminals of the HEMT, while the gate biases V.sub.G1,
V.sub.G2, and V.sub.G3 modulate the resonant 2D plasmonic modes and
the detector response. In this scheme, the THZ fields also couple
capacitively to all terminals, though the antenna is directly
connected to S and D. See G. C. Dyer et al., Proc. of SPIE 8363,
83630T (2012). Alternatively, a broadband antenna with or without a
hyper-hemispherical lens can be used to improve the coupling
efficiency. For example, the broadband antenna can be a
log-periodic antenna with a physical diameter of order millimeters.
For example, the lens can comprise a material that is transparent
to the incident radiation, such as silicon. The lens can narrow the
beam spot illuminating the active area of the antenna and improve
impedance matching of the antenna to the medium of the incident
electromagnetic field, thereby enhancing detector response.
Exemplary Plasmonic Interferometer
As an example of the invention, a plasmonic interferometer with an
integrated resonant homodyne mixing element based upon a
GaAs/AlGaAs HEMT with multiple gate terminals was fabricated. FIG.
3(a) is a scanning electron micrograph of the two-path plasmonic
interferometer where gate G2 of a HEMT defines the mixing element
and source-side Path S and drain-side Path D are tuned by G1 and
G3, respectively. In this interferometer, the gates are all
approximately 2 .mu.m wide and separated by 2 .mu.m. The distance
between the Ohmic contacts S and D is 14 .mu.m. FIGS. 3(b) and 3(c)
show the same device but with G1 and G3, respectively, defining the
mixing region.
FIG. 4 shows a transmission line circuit of the plasmonic
interferometer in FIGS. 2 and 3, representing a pair of 2D
plasmonic cavities coupled to a plasmonic mixing element. While the
equivalent circuit describes the invention as-realized in a HEMT,
it also generally depicts a plasmonic interferometer where, for
example, the mixing element could be a discrete component coupled
with 2D plasmonic waveguides. This representation of a 2D plasmonic
HEMT is analogous to the optical Mach-Zehnder interferometer in
FIG. 1 provided that the plasmonic cavities in Path S and Path D
are driven in phase with equal amplitude and the variable
inductances and resistances in each cavity are independently
tunable. A local oscillator (LO) field is coupled to the mixer to
produce a down converted, or rectified, direct current (DC) signal
by mixing with the fields incident from Path D and Path S. This
homodyne mixing response containing two signal paths that are
effectively 180 degrees out-of-phase can be understood through
analyzing the non-linear response of a plasmonic HEMT as
follows.
Resonant Plasmonic Homodyne Mixing in HEMTs
A resonant plasmonic photoresponse in the HEMT as shown in FIGS. 2
and 3 under THz illumination may arise from several mechanisms.
Recent studies have revealed a bolometric THz response mechanism,
while a photovoltage may also result from THz excitation when the
2DEG is at or near depletion. See V. M. Muravev and I. V.
Kukushkin, Appl. Phys. Lett. 100, 082102 (2012); G. C. Dyer et al.,
Appl. Phys. Lett. 97, 193507 (2010); G. C. Dyer et al., Appl. Phys.
Lett. 100, 083506 (2012); G. C. Dyer et al., Phys. Rev. Lett. 109,
126803 (2012); and G. C. Dyer et al., Nature Photon. 7, 925 (2013).
The analysis below assumes the latter mechanism, a resonant
plasmonic homodyne mixing photoresponse.
The time-averaged mixing signal under THz illumination can be
described in terms of the in-plane plasmonic voltages coupled to a
region of 2DEG,
.differential..times..times..differential..differential..times..different-
ial..times..function..function..differential..function..differential..time-
s..function. ##EQU00009## See A. Lisauskas et al., J. Appl. Phys.
105, 114511 (2009); W. Knap et al., J. Infrared, Milli., and THz
Waves 30, 1319 (2009); and S. Preu et al., J. Appl. Phys. 111,
024502 (2012). The conductance G.sub.DS and resistance
R.sub.DS=1/G.sub.DS between drain D and source S can be found from
DC transport measurements. The conductance and resistance found
from two-point transport measurements includes series contributions
from contacts and channel access regions in addition to a region of
the HEMT channel tuned by a gate. However, when a gate is biased
near its threshold voltage, the transport properties of the channel
below the gate dominate over additional series contributions. In
this limit, G.sub.DS and R.sub.DS can then be taken to describe the
transport in the plasmonic mixing region. The time dependent
voltages in Eq. (1) represent the THz fields coupled from opposing
edges (contacts) to the mixing region below a gate biased near
depletion. For generality, it is assumed that there can be more
than one gate, with Gj denoting the j.sup.th gate. The LO voltage
.differential.V.sub.LO(t) is capacitively coupled from Gj to the
2DEG, while .differential.V.sub.D(t)-.differential.V.sub.S(t) is
the difference of the THz near fields coupled to the drain and
source sides of the depleted region below gate Gj. Here
.differential.V.sub.D(t) and .differential.V.sub.S(t) are treated
as fully independent signals. Because the polarity of the net
photovoltage will depend upon which side of the mixing region the
2DEG generates a larger shift in 2DEG chemical potential, these two
independent rectified signals are subtracted rather than added.
This produces the effective, built-in 180 degree phase offset
between the two signal paths.
With G2 of a three-gate GaAs/AlGaAs HEMT tuned to deplete the 2DEG
below it as illustrated in FIG. 3(a), rectification takes place
both at the left edge of G2 where the signal from Path D couples to
the central mixing region as well as at the right edge of G2 where
the signal from Path S couples to the mixing region. Thus, the DC
potential .differential.V.sub.DS arises due to the difference
between the rectified voltages on the drain-side of G2 and the
source-side of G2. One of the underlying assumptions in this model
is a loss of coherence between the two plasmonic signal channels
when the mixing region of the 2DEG between them is biased near
depletion. Modeling by Davoyan and Popov indicates that as
n.sub.2DEG.fwdarw.0, the plasmon near field amplitude decays
rapidly from the edges of this region into its center. See A. R.
Davoyan, V. V. Popov, and S. A. Nikitov, Phys. Rev. Lett. 108,
127401 (2012); and A. R. Davoyan, and V. V. Popov, Opt. Commun.
315, 352 (2014). This isolates the plasma excitations at opposing
edges from one another, and is consistent with the experimental
assumption that these decoupled plasmonic fields produce
independent mixing signals.
While in FIG. 3(a) G2 defines the mixing region of the device as
shown, in fact any of the gates Gj can induce a plasmonic mixing
region. In FIGS. 3(b) and 3(c), alternative possibilities where G1
and G3, respectively, induce the mixing region are illustrated. The
three possible choices for plasmonic mixing region of this device
are explored through a combination of transport and photoresponse
measurements at 8 K in FIGS. 5 and 6. Measurements of the device
transport were performed using a lock-in amplifier (LIA) to source
4.0 mV at 75.0 Hz to a 5.1 kOhm load resistor in series with the
sample maintained at 8 K in a cryostat. The voltage drop across the
load resistor was measured using the LIA to determine the device
conductance as the sample gate biases were tuned. In FIG. 5(a), the
device conductance as the voltage applied to G1 of the three-gate
HEMT in FIGS. 3(a)-(c) is tuned is shown. Though this two-point
measurement includes contact resistances as well as series
contributions from wire bonds, several key features directly
related to the HEMT channel are evident. There is a discontinuity
in the conductance near V.sub.G1=-0.95 V that indicates the
presence of a parallel conduction channel in the device. In fact,
the GaAs/AlGaAs heterostructure in this device had two quantum
wells with a combined 2D electron density of 4.0.times.10''
cm.sup.-2 that conducted in parallel. This discontinuity feature
results from the depletion of the quantum well nearest to the gate.
The full depletion of both quantum wells below G1 is evident around
V.sub.G1=-2.60 V. In this regime, transport in the region
immediately below G1 dominates the system and contact resistances
are negligible in comparison.
The DC measurement of the device conductance is connected with the
expected THz photoresponse through Eq. 1. The factor
.times..differential..differential..times..times. ##EQU00010## in
Eq. 1 relates the DC transport of a HEMT to its plasmonic mixing
response, and is plotted in FIG. 5(b) as calculated from the
conductance in FIG. 5(a). To verify that Eq. 1 and its
corresponding transport measurement in FIG. 5(b) accurately
describe the plasmonic mixing response, the photoresponse plotted
in FIG. 5(c) was measured at 8 K with a 0.270 THz signal
quasi-optically steered and focused on the device at normal
incidence to the GaAs substrate. The external responsivity was
calculated using the THz power incident on the window of the
cryostat to normalize the measured voltage signal. Because this
definition of the responsivity neglects window losses as well as
power focused outside of the active area of the antenna, it should
be understood as lower bound estimate of the detector
responsivity.
A broadband THz antenna and a Si lens was used to improve the
coupling efficiency. See G. C. Dyer et al., Proc. of SPIE 8363,
83630T (2012). The incident THz radiation was linearly polarized
orthogonal to the HEMT channel between S and D contacts in order to
match the co-polarization axis of the antenna. While this
polarization weakly excites plasmons along the HEMT channel in the
absence of an antenna, for the chosen antenna layout this
polarization provides optimal plasmonic coupling to the incident
THz field.
A LIA modulated a continuous wave Schottky diode multiplier
millimeter wave source (Virginia Diodes, Inc.) at 196.7 Hz and also
measured the photovoltage generated between the source and drain
terminals of the device under 0.270 THz illumination.
Interestingly, circuit loading effects due to the HEMT RC time
constant under typical bias conditions can become significant
around several kHz modulation and reduce the measured
photoresponse. See M. Sakowicz et al., J. Appl. Phys. 110, 054512
(2011). Thus the conventional circuit RC limited bandwidth is on
the order of kHz, yet underdamped plasma excitations nonetheless
provide coupling of THz fields to a high-resistance mixing
region.
Through comparison of FIGS. 5(b) and (c), it is evident that the
measured photovoltage correlates strongly with the calculated
transport curve,
.times..differential..differential..times..times. ##EQU00011## Both
data sets have maxima where the upper and lower quantum well
channels below G1 are depleted, and also demonstrate an
approximately three order of magnitude dynamic range. Although the
plasmonic mixing response shown in FIG. 5 is largely unsurprising
given the many demonstrations of this mechanism in highly varied
transistor designs, material systems, and temperature ranges,
definitively establishing the origin of this photoresponse provides
the basis for describing the operation of a two-path plasmonic
interferometer. See D. Coquillat et al., Opt. Express 18, 6024
(2010); S. Preu et al., IEEE Trans. on THz Sci. and Tech. 2, 278
(2012); W. Knap et al., Appl. Phys. Lett. 81, 4637 (2002); W. Knap
et al., J. Infrared, Milli., and THz Waves 30, 1319 (2009). F.
Teppe et al., Appl. Phys. Lett. 87, 052107 (2005); A. El Fatimy et
al., Appl. Phys. Lett. 89, 131926 (2006); A. Shchepetov et al.,
Appl. Phys. Lett. 92 (2008); V. V. Popov et al., Appl. Phys. Lett.
98, 153504 (2011); P. Foldesy, Opt. Lett. 38, 2804 (2013); P.
Foldesy, J. Appl. Phys. 114, 114501 (2013). Asymmetry in the
plasmonic signals coupled to the mixing region,
.differential.V.sub.D(t)-.differential.V.sub.S(t).noteq.0, is
required for generating a non-zero photovoltage. See V. V. Popov et
al., Appl. Phys. Lett. 99, 243504 (2011); and T. Watanabe et al.,
Solid-State Electronics 78, 109 (2012). One means to explore
introducing asymmetry into the device is by systematically voltage
biasing each of the three gates.
In FIG. 6, the transport and responsivity characteristics at 8 K of
the HEMT are compared as one of the three gates is tuned
independently while the other two are fixed at ground potential.
The transport curves corresponding to Eq. 1 that are plotted in
FIG. 6(a) are all nearly identical, consistent with the HEMT
channel being homogeneous across the device and all three gates
sharing an identical 2 .mu.m width. Thus, the differences in the
0.270 THz responsivity shown in FIG. 6(b) arise due to asymmetry in
the device induced via the applied gate bias. The responsivity with
either gate G1 or gate G3, respectively, tuned is nearly identical
in amplitude, but opposite in polarity. Taking G1 to define the
mixing region as illustrated in FIG. 3(b), there are two plasmonic
paths feeding into this mixing region: a path formed between S and
G1 and a path formed between D and G1. Because these paths are
different lengths, 2 .mu.m vs. 10 .mu.m, the phase and amplitude of
monochromatic plasma waves impinging on the mixing region below G1
from opposing sides will, in general, be non-identical. This
produces a net photoresponse because
.differential.V.sub.D(t)-.differential.V.sub.S(t).noteq.0. The
scenario is similar when G3 defines the mixing region as shown in
FIG. 3(c), but now the short and long plasmonic paths have
exchanged relative positions in comparison to the first example.
Consistent with the measured data, this inverts the signal polarity
but leaves its amplitude largely unaffected.
A third possibility, pictured in FIG. 3(a), utilizes gate G2 to
define the mixing region. In this case, the device is essentially
symmetric about gate G2, though fabrication imperfections or
misalignment of the incident radiation can introduce asymmetries.
Here the photoresponse should be relatively weaker since the phase
and amplitude of monochromatic plasma waves impinging on the mixing
region from both paths will be nearly identical such that
.differential.V.sub.D(t)-.differential.V.sub.S(t).apprxeq.0. In
FIG. 6(b) the photoresponse with G2 tuned has a smaller amplitude,
though its measureable amplitude indicates some asymmetry in the
system under THz irradiation. Nonetheless, this is the most
near-to-balanced configuration and also offers independent
tunability of both Path D and Path S. Using this configuration, the
operation of a monolithically integrated, balanced two-path
plasmonic interferometer is described below.
Two-Path Plasmonic Interferograms
With G2 biased to deplete the 2DEG below it, the plasmonic paths
between S and G2 (Path S) and D and G2 (Path D) can be described in
terms of tunable electrical lengths. Each of these paths is 6 .mu.m
long, with 2 .mu.m regions below gates G1 and G3 that can be
voltage tuned. It is these sections below gates G1 and G3 that are
of greatest interest, and it is useful to first relate applied gate
voltages to 2DEG densities. Assuming a parallel plate capacitance
between each gate and the 2DEG,
.times..times..times..times..times. ##EQU00012## where n.sub.0 is
the intrinsic 2DEG density of 4.0.times.10.sup.11 cm.sup.-2 and
V.sub.th is the threshold voltage where the 2DEG is depleted,
V.sub.th.apprxeq.-2.60V. Since the equivalent distributed circuit
elements in FIG. 3(a) depend directly upon n.sub.1,3, the
complex-valued transmission line propagation constants for Path S
and Path D, q.sub.S,D=-i {square root over
(i.omega.C.sub.1,3(i.omega.L.sub.1,3+R.sub.1,3))}, (3) can be
defined for the voltage-tuned regions below G1 and G3,
respectively. Here the distributed kinetic inductance
L.sub.1,3=m*/e.sup.2n.sub.1,3, distributed resistance
R.sub.1,3=L.sub.1,3/.tau. and distributed 2DEG capacitance
C.sub.1,3=.epsilon.q.sub.S,D(1 coth q.sub.S,Dd) where m* is the
electron effective mass of 0.067 m.sub.e, e is the electron charge,
.tau. is the plasmon damping time, .epsilon. is the permittivity of
GaAs, and d is the separation between the gates and the 2DEG. See
G. R. Aizin and G. C. Dyer, Phys. Rev. B 86, 235316 (2012). The
inductance and resistance follow from the Drude model. Because the
plasmonic fields surrounding the 2DEG generally have a longitudinal
electric field component, the capacitance depends upon q as well as
d. However, in the long wavelength limit (q.sub.S,D d<<1)
where the gate screens the plasmon, C.sub.1,3=.epsilon./d, a
parallel plate capacitance. In general, Eq. 3 is a transcendental
equation, though it is identical to the standard definition of the
propagation constant in transmission line theory as written in
terms of equivalent circuit parameters. Though the total electrical
lengths of Path S and Path D will also include the 4 .mu.m of
untuned 2DEG, it is sufficient to consider only the tuned regions
to find the difference in electrical lengths. Thus, the relevant
electrical lengths for Paths S and D are,
.theta..sub.S,D=aq'.sub.S,D, (4) where
q.sub.S,D=q'.sub.S,D+iq''.sub.S,D, q'.sub.S,D and q''.sub.S,D are
real, and a=2 .mu.m. Then the difference in electrical lengths of
the two paths is .DELTA..theta..sub.S,D, =a(q'.sub.D-q'.sub.S).
Physically, as either G1 or G3 is tuned towards threshold voltage,
the electron density is decreased, the 2DEG (kinetic) inductance
increases, the plasmon wavelength decreases, and the propagation
constant increases.
The interferometric plasmonic signal with Path S and Path D
independently controlled is illustrated in FIGS. 7(a) and (b).
These experimental measurements were performed at 8 K for
excitation frequencies of 0.270 and 0.360 THz, respectively, with
V.sub.G2=-2.55 V. Because the gate voltage, the 2DEG density, the
plasmon propagation constant, and the electrical length are all
directly related by Eqs. 2-4, any of these may effectively
parameterize the tuning of Paths S and D. In FIG. 7, the electrical
lengths .theta..sub.SD corresponding to Path S and Path D are used
in plotting the plasmonic interferogram. The diagonal lines from
the lower left to upper right corners of FIGS. 7(a) and (b)
indicate where .DELTA..theta.=0. This can be viewed as a 180 degree
phase shift between the two identical paths when otherwise excited
identically. For the balanced two-path interferometer, this
diagonal marks where the signal should vanish as well as the
boundary about which the signal should have anti-mirror symmetry.
This is equivalent to stating that the signal
S(.theta..sub.S,.theta..sub.D) obeys the relation
S(.theta..sub.1,.theta..sub.2)=-S(.theta..sub.2,.theta..sub.1).
Though the experimental results plotted in FIGS. 7(a) and (b) do
not precisely follow this rule as would be the case in ideal
balancing of the two paths, the qualitative picture nonetheless is
indicate of anti-mirror symmetry. The signal tends to weaken then
change polarity along .DELTA..theta.=0 and for each positive signal
polarity resonance at a coordinate (.theta..sub.1,.theta..sub.2)
there tends to be a companion resonance at
.theta..sub.2,.theta..sub.1) with negative polarity.
The quantity Re[.differential.V.sub.D-.differential.V.sub.S]
calculated using a plasmonic transmission line model as shown in
FIG. 4 is plotted in FIGS. 7(c) and (d) for excitation frequencies
of 0.270 and 0.360 THz using the plasmonic transmission line model.
Here it is assumed the antenna functions as a lumped element
voltage source with an internal impedance found from its radiation
resistance. See G. C. Dyer et al., Phys. Rev. Lett. 109, 126803
(2012). Additionally, because the equivalent circuit sources
driving the LO, Path S and Path D are in-phase, the real parts of
the calculated plasmonic transmission line voltages can be
calculated to emulate the anticipated plasmonic mixing response.
There is very good agreement between experimental and model
interferograms in FIGS. 7(a) and (c) using this approach, with
several resonances matched in polarity observable along both the
vertical and horizontal axes. However, the model interferogram in
FIG. 7(d) does not match the experimental interferogram in FIG.
7(b) as well. Although the lower order resonances seen at the
shortest electrical lengths have the same polarity in FIGS. 7(b)
and (d), the model calculations predict additional higher order
resonances that are not observed experimentally. Part of the
discrepancy may arise from higher experimental plasmonic damping
rates than the damping rate corresponding to an electron mobility
of 100,000 cm.sup.-2/V-s used in the model calculations. As the
electrical length is increased by gate tuning, the losses increase,
the resonances broaden, and the signal amplitude decreases. This is
a qualitative feature of all plots in FIG. 7, and it is possible
that the higher order modes in FIG. 7(d) cannot be resolved.
To further demonstrate the invention, a second exemplary device
design, shown in FIG. 8(a), was considered where the two plasmonic
paths are independently tunable four-period plasmonic crystals. See
G. C. Dyer et al., Nature Photon. 7, 925 (2013). Here G2 is a
single 2 .mu.m gate, and G1 and G3 tune Path S and Path D,
respectively, using four identically tuned 2 .mu.m wide gate
stripes separated by 2 .mu.m each. The distance between the Ohmic
contacts S and D is 34 .mu.m. In this device, the gate tuning of
plasma wave propagation cannot be interpreted as a simple change of
electrical length. Because plasmons are Bragg scattered in this
short periodic lattice, a crystal quasi-momentum defined by the
Bloch wavevector better describes plasma wave dispersion than the
propagation constant of a plasmon below G1 or G3. The
experimentally measured plasmonic interferogram in the left frame
of FIG. 8(b) with 0.345 THz excitation and G2 biased to
V.sub.G2=-2.80 V at 8 K is therefore plotted in terms of gate
voltages V.sub.G1 and V.sub.G3. This plasmonic interferometer can
be understood as an in-situ plasmonic spectrometer for a more
complicated plasmonic heterostructure than the device shown in
FIGS. 3(a)-(c). As before, plasmonic homodyne mixing takes place at
the left and right edges of G2, but multi-period structures between
S and G2 and D and G2 control the signals coupled to this mixing
region. Despite the additional complexity of Paths S and D, a
striking anti-mirror symmetry about V.sub.G1=V.sub.G3 where
S(V.sub.1,V.sub.2)=-S(V.sub.2,V.sub.1) is observed, indicating a
well-balanced two-path plasmonic system.
A model interferogram of the calculated quantity
Re[.differential.V.sub.D-.differential.V.sub.S] is plotted in the
right frame of FIG. 8(b) for an excitation frequency of 0.345 THz
using a plasmonic transmission line model to describe the
four-period plasmonic crystals in Path S and Path D. Here a 2DEG
density of 4.5.times.10'' cm.sup.-2, about 10% larger than the 2DEG
density determined from Hall measurements, and an electron mobility
of 600,000 cm.sup.-2/V-s, consistent with the mobility found from
Hall measurements, were used in the model calculation. Although the
overall agreement with experiment is largely qualitative in nature,
the expected anti-mirror symmetry about V.sub.G1=V.sub.G3 where
S(V.sub.1,V.sub.2)=-S(V.sub.2,V.sub.1) is present. The most
significant discrepancies between the model and experiment in FIG.
8(b) likely arise as a result of approximating the THz excitation
as a lumped source in the transmission line model rather than a
more realistic distributed excitation. While the transmission line
approach predicts the resonant modes of the system with adequate
fidelity, the exact plasmonic field amplitudes of Path S and D at
the edges adjacent to the mixer will depend non-trivially upon the
THz excitation of each plasmonic crystal. The THz coupling impacts
not only the amplitudes of resonances, but also linewidths since
radiative damping is a significant broadening mechanism. Moreover,
radiative damping rates will generally not be identical for all
modes in the system. A lumped excitation is a reasonable
approximation for plasmonic cavities with only several plasmonic
elements, but limits the validity of the transmission line approach
for modeling the plasmonic near fields of more complicated
devices.
Several additional features in FIG. 8(b) prompt further
consideration. First, in comparison to FIG. 7, many additional
modes are observed with only a slight increase in excitation
frequency. This is understood in part by comparing the 6 .mu.m
plasmonic path lengths in the device shown in FIG. 3(a) to the 18
.mu.m path lengths in device shown in FIG. 8(a). The fundamental
mode of the 18 .mu.m path occurs at a lower frequency than that of
the 6 .mu.m path, and therefore a relatively denser set of higher
order modes is anticipated for a given excitation frequency.
Alternately, the coupling of four gated regions of the 2DEG in the
device shown in FIG. 8(a) lifts a four-fold degeneracy, and
therefore approximately four modes are expected for every one
observed in the device of FIG. 3(a). Additionally, the highest
intensity signal is observed with significant tuning of gate
voltage. This would be analogous to observing the largest signal in
FIG. 7 at any electrical length but the smallest measured. One
possibility consistent with a recent study of localized modes in
terahertz plasmonic crystals is that specific modes in the spectrum
couple less well to the mixing region due to their confinement
adjacent to an Ohmic contact, either source S or drain D. See G. C.
Dyer et al., Nature Photon. 7, 925 (2013). Although the distributed
nature of the THz excitation precludes validation of this
hypothesis using a lumped source to model the plasmonic near field
amplitude, the non-monotonic behavior of signal intensities is
suggestive of the localization of plasmon modes in Path S and Path
D.
As described above, on-chip plasmonic interferometry can be
integrated with a widely-used plasmonic detection technique.
Although the exemplary devices used an antenna to provide the
distributed excitation of the signal channels and the LO of the
plasmonic mixer, waveguide-coupled structures can also be used if
the LO and signal channels are suitably isolated, as illustrated in
FIG. 9. See W. F. Andress et al., Nano Lett. 12, 2272 (2012); and
K. Y. M. Yeung et al., Appl. Phys. Lett. 102, 021104 (2013), which
are incorporated herein by reference. The phase relationship
between the LO and signal channels is determined by the coupling of
the THz excitation to HEMT terminals. Isolation of these channels
allows for control of their relative phase and potentially a
quadrature measurement to extract both the amplitude and phase of
an incident THz signal. This possibility arises because the
plasmonic mixer is a field rather than power detector. While
intensity interferograms are often measured by bringing two paths
coincident upon a power detector, here field phase information is
partially preserved by independently generating a DC signal from
each path and reading out to a single differential channel. Prior
interferometric sensors have focused on optical techniques. As with
the optical Mach-Zehnder interferometer, the sensitivity of 2D
plasma excitations to their environment can provide a sensor
wherein a phase shift is sensitive to a sample in one of the
plasmonic paths. Therefore, the plasmonic interferometer of the
present invention enables an electro-optical approach to near-field
plasmonic sensing. Further, although the above described examples
based on GaAs/AlGaAs heterostructures require both cryogenic
cooling and a vacuum environment, other plasmonic materials such as
graphene have neither as a requirement. The electromagnetic
screening of 2D plasma waves by a metal terminal is a limiting case
of environment modifying plasmon dispersion. However, more subtle
effects, particularly in graphene, can arise due to plasmon-phonon
coupling with an adjacent material or the coupling of plasmons with
an adsorbed polymer. See Z. Fei et al., Nano Letters 11, 4701
(2011); H. Yan et al., Nature Photon. 7, 394 (2013); and Y. Li et
al., Nano Letters (2014). The plasmonic interferometer of the
present invention enables an electro-optical approach to near-field
plasmonic sensing.
Integration of interferometric elements into a voltage-tunable
microelectronic plasmonic device provides potential advantages over
existing spectroscopic techniques, particularly in the far
infrared. Though the substantial reduction in optical path length
is beneficial, the most significant advantage is provided by the
broad voltage tunability. The invention described above utilized an
intrinsic mixing mechanism to exploit the plasmonic near-field
enhancement. However, as illustrated in FIG. 4, the integration of
a discrete mixing component with plasmonic elements is also viable.
See U.S. Pat. No. 8,274,058 to Wanke et al., which is incorporated
herein by reference. Provided the integrated mixer directly couples
to the near field of plasma excitations, conventional diode-based
detection elements can be used. The specific choice of technology
depends upon the compatibility of material systems and process
technologies. This enables, for example, frequency agile heterodyne
mixers that do not rely on front-end optics for spectrally
selective signal input.
Heterodyning consists of mixing a received RF signal with a LO
signal. The LO signal has a frequency that is detuned from the
frequency of the received RF signal. The mixer produces an output
signal having an intermediate frequency IF that is equal to the
difference between the frequencies of the LO and RF signals. The IF
signal is tunable through the LO frequency and can be
post-amplified and processed using conventional microwave
techniques. Further, the LO can have a fixed output power that is
generally much greater than the power of the received RF signal,
thereby producing an IF output power that is proportional to the
product of the powers of the LO and received RF signals.
The waveguide-coupled structure shown in FIG. 9 enables heterodyne
mixing whereby two different LO and RF frequencies can generate an
intermediate frequency. In this example, the incident
electromagnetic radiation RF.sub.S and RF.sub.D is applied to the
source S and drain D sides of the plasmonic interferometer via
opposing source-side and drain-side waveguides fabricated on the
chip. Voltages can be applies to gates G1 and G2 to provide
source-side and drain-side plasmonic paths in the 2DEG of the
interferometer. The central gate G2 can be biased to near depletion
to provide a plasmonic mixer in the 2DEG region under the central
gate. An LO signal having a frequency that is detuned from the
frequency of the RF.sub.S and RF.sub.D signals can be applied to
the plasmonic mixer via a central waveguide. The IF signal can be
removed through the central waveguide and a directional coupler can
be used to route the IF signal to a post processor, for example, a
spectrum analyzer.
The present invention has been described as a two-path plasmonic
interferometer with integrated detector. It will be understood that
the above description is merely illustrative of the applications of
the principles of the present invention, the scope of which is to
be determined by the claims viewed in light of the specification.
Other variants and modifications of the invention will be apparent
to those of skill in the art.
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